Module Coq.Arith.Peano_dec

Require Decidable.

Theorem O_or_S : (n:nat)({m:nat|(S m)=n})+{O=n}.
Proof.
NewInduction n.
Auto.
Left; Exists n; Auto.
Defined.

Theorem eq_nat_dec : (n,m:nat){n=m}+{~(n=m)}.
Proof.
NewInduction n; NewInduction m; Auto.
Elim (IHn m); Auto.
Defined.

Hints Resolve O_or_S eq_nat_dec : arith.

Theorem dec_eq_nat:(x,y:nat)(decidable (x=y)).
Intros x y; Unfold decidable; Elim (eq_nat_dec x y); Auto with arith.
Defined.


Index